1) \(\left(3x^2-1\right)\left(9x^4+3x^2+1\right)\)

\(=27x^6+9x^4+3x^2-9x^4-3x^2-1\)

\(=27x^6-1\) (hằng đẳng thức dạng a³ - b³)

2) \(\left(x^2-4\right)\left(x^2+2x+4\right)\left(x^2-2x+4\right)\) 

\(=\left(x-2\right)\left(x+2\right)\left(x^2+2x+4\right)\left(x^2-2x+4\right)\)

\(=\left[\left(x-2\right)\left(x^2+2x+4\right)\right].\left[\left(x+2\right)\left(x^2-2x+4\right)\right]\)

\(=\left(x^3-8\right)\left(x^3+8\right)\)

\(=x^6-64\)

a) \(\left(3x^2-1\right)\left(9x^4+3x^2+1\right)=\left(3x^2-1\right)\left[\left(3x^2\right)^2+3x^2.1+1^2\right]=\left(3x^2\right)^3-1^3=3x^6-1\)

b) \(\left(x^2-4\right).\left(x^2+2x+4\right).\left(x^2-2x+4\right)=\left(x^2-2^2\right).\left(x+2\right)^2.\left(x-2\right)^2=\left(x+2\right).\left(x-2\right).\left(x+2\right)^2.\left(x-2\right)^2=\left(x+2\right)^3.\left(x-2\right)^3\)

a) \(\left(3x-2\right)^2=\left(3x\right)^2-2.3x.2+2^2=9x^2-12x+4\)

b) \(\left(\dfrac{x}{3}+y^3\right)^2=\left(\dfrac{x}{3}\right)^2+2\dfrac{x}{3}y^3+\left(y^3\right)^2=\dfrac{x^2}{9}+\dfrac{2}{3}xy^3+y^6\)

c) \(9x^2-225=\left(3x\right)^2-\left(15\right)^2=\left(3x-15\right)\left(3x+15\right)\)

d) \(\left(2x-3y\right)^3=\left(2x\right)^3-3\left(2x\right)^23y+3.2x\left(3y\right)^2-\left(3y\right)^3=8x^3-3.4x^2.3y+6x.9y^2-27y^3=8x^3-36x^2y+54xy^2-27y^3\)

e) \(\left(2x^2+\dfrac{3}{2}\right)^3=\left(2x^2\right)^3+3\left(2x^2\right)^2\dfrac{3}{2}+3.2x^2\left(\dfrac{3}{2}\right)^2+\left(\dfrac{3}{2}\right)^3=8x^6+3.4x^4.\dfrac{3}{2}+6x^2.\dfrac{9}{4}+\dfrac{27}{8}=8x^6+18x^4+\dfrac{27}{2}x^2+\dfrac{27}{8}\)

f) \(\left(-2xy^2+\dfrac{1}{2}x^3y\right)^3=\left(-2xy^2\right)+3\left(-2xy^2\right)^2\dfrac{1}{2}x^3y+3\left(-2xy^2\right)\left(\dfrac{1}{2}x^3y\right)^2+\left(\dfrac{1}{2}x^3y\right)^3=-8x^3y^6+3.4x^2y^4.\dfrac{1}{2}x^3y-6xy^2.\dfrac{1}{4}x^6y^2+\dfrac{1}{8}x^9y^3=-8x^3y^6+6x^5y^5-\dfrac{3}{2}x^7y^4+\dfrac{1}{8}x^9y^3\)

\(a,=x^2+x+\dfrac{1}{4}\\ b,=4x^2+2x+\dfrac{1}{4}\\ c,=x^2-2+\dfrac{1}{x^2}\\ d,=4x^2+\dfrac{8}{3}x+\dfrac{4}{9}x^2\\ e,=a^2-1\\ f,=25x^4-4\)

\(a,\left(x+\dfrac{1}{2}\right)^2=x^2+x+\dfrac{1}{4}\)

\(b,\left(2x+\dfrac{1}{2}\right)^2=4x^2+2x+\dfrac{1}{4}\)

\(c,\left(x-\dfrac{1}{x}\right)^2=x^2-2+\dfrac{1}{x^2}\)

\(d,\left(\dfrac{2x+2}{3x}\right)^2=\dfrac{\left(2x+2\right)^2}{9x^2}=\dfrac{4x^2+8x+4}{9x^2}\)

\(e,\left(a-1\right).\left(a+1\right)=a^2-1\)

\(f,\left(5x^2-2\right).\left(5x^2+2\right)=25x^4-4\)

a. \(\left(x+\dfrac{1}{2}\right)^2=x^2+x+\dfrac{1}{4}\)

b. \(\left(2x+\dfrac{1}{2}\right)^2=4x^2+2x+\dfrac{1}{4}\)

c. \(\left(x-\dfrac{1}{x}\right)^2=x^2-2+\dfrac{1}{x^2}\)

d. \(\left(2x+\dfrac{2}{3x}\right)^2=4x^2+\dfrac{8}{3}+\dfrac{4}{9x^2}\)

e. (a - 1)(a + 1) = a² - 1

f. (5x² - 2)(5x² + 2) = 25x⁴ - 4 

g. (2a - 3)(2a + 3) = 4a² - 9

xin lỗi vì ko giúp đc zì !!! Tại ....... e ms lớp 6 à !!!! 

a) \(100x^2-\left(x^2+25\right)^2\)

\(=\left(10x-x^2-25\right)\left(10x+x^2+25\right)\)( Áp dụng hằng đẳng thức số 3 )

b) ko khai phân tích dc bạn ạ

c) 

dễ thế này tự suy nghĩ đi biểu k đc học những cái cơ bản ak!

a) \(\left(2x^3-y^2\right)^3\)

\(=\left(2x^3\right)^3-3\cdot\left(2x^3\right)^2\cdot y^2+3\cdot2x^3\cdot\left(y^2\right)^{^2}-\left(y^2\right)^3\)

\(=8x^9-3\cdot4x^6y^2+3\cdot2x^3y^4-y^6\)

\(=8x^9-12x^6y^2+6x^3y^4-y^6\)

b) \(\left(x-3y\right)\left(x^2+3xy+9y^2\right)\)

\(=x^3-\left(3y\right)^3\)

\(=x^3-27y^3\)

c) \(\left(x+2y+z\right)\left(x+2y-z\right)\)

\(=\left(x+2y\right)^2-z^2\)

\(=x^2+4xy+4y^2-z^2\)

d) \(\left(2x^3y-0,5x^2\right)^3\)

\(=\left(2x^3y-\dfrac{1}{2}x^2\right)^3\)

\(=8x^9y^3-6x^8y^2+\dfrac{3}{2}x^7y-\dfrac{1}{8}x^6\)

e) \(\left(x^2-3\right)\left(x^4+3x^2+9\right)\)

\(=\left(x^2-3\right)\left(4x^2+9\right)\)

\(=4x^4+9x^2-12x^2-27\)

\(=4x^4-3x^2-27\)

f) \(\left(2x-1\right)\left(4x^2+2x+1\right)\)

\(=\left(2x\right)^3-1^3\)

\(=8x^3-1\)

\(a,\left(2x^3-y^2\right)^3=8x^9-12x^6y^2+6x^3y^4-y^6\)\(b,\left(x-3y\right)\left(x^2+3xy+9y^2\right)=x^3-27y^3\)

\(c,\left(x+2y+z\right)\left(x+2y-z\right)=\left(x+2y\right)^2-z^2=x^2+4xy+4y^2-z^2\)\(d,\left(2x^3y-0,5x^2\right)^3=8x^9y^3-6x^4y^2x^2+3x^3yx^4-0,125x^6=8x^9y^3-6x^6y^2+3x^7y-0,125x^6\)

a: \(\left(3x-2\right)^2=9x^2-12x+4\)

c: \(9x^2-225=9\left(x^2-25\right)=9\left(x-5\right)\left(x+5\right)\)

a: \(\left(3x-2\right)^2=9x^2-12x+4\)

c: \(9x^2-225=\left(3x-15\right)\left(3x+15\right)\)

d: \(\left(2x-3y\right)^3=8x^3-36x^2y+54xy^2-27y^3\)

a) \(=x^3+27-54-x^3=-27\)

b) \(=8x^3+y^3\)